Let $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1,{\rm{when}}\,\,x\,\,{\rm{is }}\,{\rm{rational}}}\\ {0,{\rm{when}}\,\,x\,\,\,{\rm{irrational}}} \end{array}} \right.$ , then $\mathop {\lim }\limits_{x \to 0} f\left( x \right)$ is

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Analyzing +4 | -1

Let

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {1,\mathrm{when}\,\,x\,\,\mathrm{is }\,\mathrm{rational}}\\ {0,\mathrm{when}\,\,x\,\,\,\mathrm{irrational}} \end{array}} \right.

, then

\lim\limits_{x \to 0} f\left( x \right)

View answer and explanation

Correct option: B

Option D (None of these) is correct because the limit does not exist as the left-hand limit and right-hand limit are not equal when approaching 0.